SIMPLIFYING EXPRESSIONS WORKSHEET AND COMBINING LIKE TERMS
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Objectives of this Chapter, one should be able to:

Before we practice simplifying expressions, some new languare of algebra must be presented. A term is a number of the product of anuber and a variable raised to some power (in most cases). Additionally, the numerical coefficient of a term is the numberical factor. For example, the numberical coefficient of (3x) is the 3. Recall that 3x really mens 3 times x.
Term  Numerical Coefficient sometimes just called the coefficient 
3x, y^{3}/5 0.25ab^{3}c^{5} z y 5
 3 1/5 0.25 1 1 5

Terms with the same variable raised to exactly the same power are called Like Terms. In like manner terms that aren't like terms are called Unlike Terms.
Like Terms  Unlike Terms 
3x, 2x 6 x^{2}y, 2x^{2}y, +4x^{2}y, 2 abc, +3 abc, .025 abc
 5x, 5x^{3} 7y, 3z, 8x^{2} +6abc, 6a^{2}b^{3} 
In like terms, each variable and its exponent must match exactly, but these fractors do not have to be in the same order. For example 2x^{2}y and 3yx^{2} are like terms.
Simplifying expressions makes frequent use of the distributive property to remove parentheses.
If a " minus" sign precedes parentheses,then sign of each term inside the parentheses is changed when the distributive property is applied to remove the parenthesis itself. Examples: (2x +1) = 2x 1(5x +y z ) = +5x y +z(+x2y) = x +2y(3x4y1) = +3x +4y + 1 
following expression: 8 (7x +2 ) +3x  2(4x +7)  (3x 1) ?
First remove the parentheses  8 (7x +2 ) +3x  2(4x +7)  (3x 1 = +8 7x 2 +3x 8x 14 3x +1 
Now we need to combine like terms  +8 2 14 +1 = 7 7x +3x 8x 3x = 15x 
Now write the variable first then the numberical coefficient for the final simplification of the expression  15x 7 